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Abstract The paper drying process has the highest level of energy consumption in the pulp and paper production process. Analysis and optimization of the energy system during the paper drying process is critical for improving the energy efficiency of the entire paper mill. In the existing model for the paper drying process, the solution requires accurate boundary conditions such as the air temperature and humidity of the pocket area and the cylinder surface temperature, which are very difficult to obtain in the papermaking process. This can result in significant deviations between the model solution and the actual production process. This paper focuses on the single-tier dryer cylinder-based paper drying process that has been widely used with high-speed papermaking machines in recent years. A mathematical model is proposed based on real-time data. The verification via industrial production demonstrates that the proposed model is reliable for the paper drying process. Based on the simulation results, two optimization operations have been proposed. The energy consumption decreases from 1.51 t steam/t paper to 1.44 t steam/t paper, 4.6% of the steam and 1.26 × 106 RMB can be saved for a medium-scale paper mill with the annual production capacity of 105 t paper. Highlights • Mathematical model for the single-tier cylinder based paper drying process is proposed. • Both the steam-condensate system and the paper drying process are considered. • The simulation results are verified by the industrial data from a papermaking enterprise. [ABSTRACT FROM AUTHOR]

Soil reinforcement using geosynthetics is an efficient and cost-effective solution for a variety of geotechnical structures. Along with the increasing use of geosynthetics, there is a need to expand and enhance the design methodologies for these elements, which are still frequently based on conservative limit equilibrium approaches. In this paper, a bibliometric analysis was conducted on geosynthetic-reinforced soil structures (GRS), identifying the state of the art, research trends, and other indicators. The data were obtained from the Scopus platform and processed by VOSViewer v1.6 software. The initial search comprised 552 papers and the screening process selected 516 relevant papers from 1992 to October 2023. The study analyzed the occurrence of publications by year, keyword trends, authors, citations/co-citations, and bibliographic coupling. Then, a focus was given to 3D modeling research on geosynthetics, highlighting the dominant modeling techniques, material properties, and design challenges in GRS. The bibliometric analysis provided a crucial guideline in the identification of relevant papers and research trends, and a series of conclusions were presented regarding the 3D modeling techniques, choice of material properties, and boundary conditions. [ABSTRACT FROM AUTHOR]

The overall reliability of a power transformer depends to a great extent on the sound operation of the bushings thereof. Oil impregnated paper (OIP) insulated bushings have been in use for a long time now. In many situations, it becomes necessary to avoid OIP insulation in bushings. In the recent past, a new technological breakthrough has been achieved whereby the OIP is replaced by epoxy resin impregnated crepe paper (RIP) insulation. This new system has several advantages over OIP and has now become the insulation of choice. However, its long time thermal and electrical performance need to be carefully assessed. This paper reports the results of a study of temperature distribution in the body of insulation, based on the ac conductivity of RIP insulation. A method of computing the maximum thermal voltage of this system is also given. [ABSTRACT FROM AUTHOR]

Abstract: The multiple-relaxation-time (MRT) lattice Boltzmann method (LBM) with multi-reflection solid boundary conditions is used to study anisotropic permeabilities of a carbon paper gas diffusion layer (GDL) in a fuel cell. The carbon paper is reconstructed using the stochastic method, in which various porosities and microstructures are achieved to simulate different samples. The simulated permeability and tortuosity show anisotropic characteristics of the reconstructed carbon papers with in-plane permeability higher than through-plane, and in-plane tortuosity lower than through-plane. The calculated permeabilities are in good agreement with existing measurements. The relationship between the permeability and the porosity is fitted with empirical relations and some fitting constants are determined. Furthermore, the obtained relationship of tortuosity and porosity is used in a fractal model for permeabilities. The results indicate that the fractal model and the Kozeny–Carman equation provide similar predictions on the through-plane permeability of the carbon paper GDL. [Copyright &y& Elsevier]

In a series of papers which are either published [Hadjesfandiari, A., Dargush, G. F., 2011a. Couple stress theory for solids. Int. J. Solids Struct. 48 (18), 2496–2510; Hadjesfandiari, A., Dargush, G. F., 2013. Fundamental solutions for isotropic size-dependent couple stress elasticity. Int. J. Solids Struct. 50 (9), 1253–1265.] or available as preprints [Hadjesfandiari, A., Dargush, G. F., 2010. Polar continuum mechanics. Preprint arXiv:1009.3252; Hadjesfandiari, A. R., Dargush, G. F., 2011b. Couple stress theory for solids. Int. J. Solids Struct. 48, 2496–2510; Hadjesfandiari, A. R., 2013. On the skew-symmetric character of the couple-stress tensor. Preprint arXiv:1303.3569; Hadjesfandiari, A. R., Dargush, G. F., 2015a. Evolution of generalized couple-stress continuum theories: a critical analysis. Preprint arXiv:1501.03112; Hadjesfandiari, A. R., Dargush, G. F., 2015b. Foundations of consistent couple stress theory. Preprint arXiv:1509.06299] Hadjesfandiari and Dargush have reconsidered the linear indeterminate couple stress model. They are postulating a certain physically plausible split in the virtual work principle. Based on this postulate they claim that the second-order couple stress tensor must always be skew-symmetric. Since they do not consider that the set of boundary conditions intervening in the virtual work principle is not unique, their statement is not tenable and leads to some misunderstandings in the indeterminate couple stress model. This is shown by specifying their development to the isotropic case. However, their choice of constitutive parameters is mathematically possible and we show that it still yields a well-posed boundary value problem. [ABSTRACT FROM AUTHOR]

The purpose of the present note is to point out mathematical mistakes in some published papers on boundary value problems to prevent usage of mistaken results and methods by mathematicians. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This document is an editorial for a special issue of the journal Mathematics titled "Differential Equations of Mathematical Physics and Related Problems of Mechanics." The special issue covers a range of topics related to differential equations in mathematical physics and mechanics, including wave equations, spectral theory, scattering, and inverse problems. The editorial provides a summary of the published papers in the special issue, highlighting their contributions to the field. The document emphasizes the importance of the special issue in covering both applied and fundamental aspects of mathematics, physics, and their applications in various fields. The author expresses gratitude to the authors, reviewers, assistants, associate editors, and editors for their contributions to the special issue. The report does not provide specific details about the content of the papers or the nature of the special issue. [Extracted from the article]

Abstract: We study the formation of multi-armed spirals and multi-pairs antispirals in spatial rock–paper–scissors games with mobile individuals. We discover a set of seed distributions of species, which is able to produce multi-armed spirals and multi-pairs antispirals with a finite number of arms and pairs based on stochastic processes. The joint spiral waves are also predicted by a theoretical model based on partial differential equations associated with specific initial conditions. The spatial entropy of patterns is introduced to differentiate the multi-armed spirals and multi-pairs antispirals. For the given mobility, the spatial entropy of multi-armed spirals is higher than that of single armed spirals. The stability of the waves is explored with respect to individual mobility. Particularly, we find that both two armed spirals and one pair antispirals transform to the single armed spirals. Furthermore, multi-armed spirals and multi-pairs antispirals are relatively stable for intermediate mobility. The joint spirals with lower numbers of arms and pairs are relatively more stable than those with higher numbers of arms and pairs. In addition, comparing to large amount of previous work, we employ the no flux boundary conditions which enables quantitative studies of pattern formation and stability in the system of stochastic interactions in the absence of excitable media. [Copyright &y& Elsevier]

In this paper, Caputo boundary value problems of order 3 < ζ ≤ 4 are investigated on the interval [0, 1]. By Guo-Krasnoselskii fixed point theorem, some criteria of existence and multiplicity of positive and decreasing solutions are established. The main novelty of the paper lies in its capability to achieve positive solutions while the corresponding Green’s function changes sign. Finally, two examples are provided to illustrate the application of these results. [ABSTRACT FROM AUTHOR]

Abstract: In (2012), Leonetti and Siepe [10] considered solutions to boundary value problems of some anisotropic elliptic equations of the type Under some suitable conditions, they obtained an integrability result, which shows that higher integrability of the boundary datum forces solutions to have higher integrability as well. In the present paper, we consider -obstacle problems of the nonhomogeneous anisotropic elliptic equations under some controllable growth and monotonicity conditions. We obtain an integrability result, which can be regarded as a generalization of the result due to Leonetti and Siepe. [Copyright &y& Elsevier]

The effect of interaction between liquid crystal (LC) and photoalignment material on the speed of optical rewriting process is investigated. The theoretical analysis shows that a smaller frank elastic constant K22 of liquid crystal corresponds to a larger twist angle, which gives rise to a larger rewriting speed. Six different LC cells with the same boundary conditions (one substrate is covered with rubbed polyimide (PI) and the other with photo sensitive rewritable sulfuric dye 1(SD1)) are tested experimentally under the same illumination intensity (450 nm, 80 mW/cm2). The results demonstrate that with a suitable liquid crystal, the LC optical rewriting speed for e-paper application can be obviously improved. For two well known LC materials E7 (K22 is larger) and 5CB (K22 is smaller), they require 11 s and 6 s corresponding to change alignment direction for generating image information. [ABSTRACT FROM AUTHOR]

Abstract: The aim of this paper is twofold: First, we characterize an essentially optimal class of boundary operators Θ which give rise to self-adjoint Laplacians in with (nonlocal and local) Robin-type boundary conditions on bounded Lipschitz domains , , . Second, we extend Friedlander''s inequalities between Neumann and Dirichlet Laplacian eigenvalues to those between nonlocal Robin and Dirichlet Laplacian eigenvalues associated with bounded Lipschitz domains Ω, following an approach introduced by Filonov for this type of problems. [Copyright &y& Elsevier]

This paper deals with non-constant positive steady-state solutions of a predator-prey system with non-monotonic functional response, also called Holling type-IV interaction terms, and diffusion under the homogeneous Neumann boundary condition. We first establish positive upper and lower bounds for such solutions, and then study their non-existence, global existence and bifurcation. [ABSTRACT FROM AUTHOR]

In this paper, we consider the boundary value problem for the Sturm-Liouville type equation with the fixed delay π/2 and a non zero initial function under transmission conditions at the delay point. We study the case when all parameters within the transmission conditions are known and the potential function is known on the interval (0, π/2). We will prove the uniqueness theorem from two spectra, first with Neumann boundary conditions and second with Cauchy boundary condition. Additionally, we will present an algorithm for the construction of the potential function over the interval (π/2, π). [ABSTRACT FROM AUTHOR]

Electromagnetic cloaking has been widely studied in recent years. In this review article we explain the basic principles of numerical modeling and characterization of selected broadband cloaking structures that are designed to operate within the microwave frequency range. Because the cloaks are periodical structures, the numerical modeling is simplified by employing symmetry boundary conditions. The modeling and characterization are done both with frequency-domain and time-domain simulations. Various experimental results are also compared to numerical results. © 2012 Wiley Periodicals, Inc. Int J RF and Microwave CAE 22:483-495, 2012. [ABSTRACT FROM AUTHOR]

Abstract: In this note, we point out an error in the recently published article [R.K. Mohanty, M.K. Jain, D. Dhall, A cubic spline approximation and application of TAGE iterative method for the solution of two-point boundary value problems with forcing function in integral form, Appl. Math. Model. 35 (2011) 3036–3047] and then correct it. [Copyright &y& Elsevier]

The high pressure structure of α-oxalic acid di-hydrate shows a prototypical behaviour of acid to base proton transfer reaction. The solid state transformation has been characterized by neutron and X-ray diffraction as well as by quantum chemical calculations with periodic boundary conditions. The two resonant configurations playing the most important role in the hydrogen bond mechanism, i.e.a neutral and a charge transfer configuration, are interchanged by modifying the pressure on the system. A different behaviour is predicted for the less common β form, despite an apparently similar packing motif. Implications for the characterization of hydrogen bonds in the solid state are discussed as well as the possibility of estimating internal energy variations from experimental measurements. [ABSTRACT FROM AUTHOR]

In studying boundary value problems and coupled systems of fractional order in (1 , 2 ] , involving Hilfer fractional derivative operators, a zero initial condition is necessary. The consequence of this fact is that boundary value problems and coupled systems of fractional order with non-zero initial conditions cannot be studied. For example, such boundary value problems and coupled systems of fractional order are those including separated, non-separated, or periodic boundary conditions. In this paper, we propose a method for studying a coupled system of fractional order in (1 , 2 ] , involving fractional derivative operators of Hilfer and Caputo with non-separated boundary conditions. More precisely, a sequential coupled system of fractional differential equations including Hilfer and Caputo fractional derivative operators and non-separated boundary conditions is studied in the present paper. As explained in the concluding section, the opposite combination of Caputo and Hilfer fractional derivative operators requires zero initial conditions. By using Banach's fixed point theorem, the uniqueness of the solution is established, while by applying the Leray–Schauder alternative, the existence of solution is obtained. Numerical examples are constructed illustrating the main results. [ABSTRACT FROM AUTHOR]

This paper introduces a topology optimization approach based on the virtual element method (VEM), incorporating uncertainties. The objective of this optimization process is to design an optimal material layout for problems governed by linear elasticity equations to minimize the volume while satisfying probabilistic compliance constraints. The VEM is used to solve the boundary value problem in reliability-based topology optimization (RBTO). In the comparison between the VEM and the standard finite element method (FEM), a key difference emerges in the absence of explicitly defined shape functions tied to discrete degrees of freedom in VEM. Unlike FEM, VEM directly constructs the discrete bilinear form and load linear form without the need for computing shape function derivatives within the elements. This flexibility accommodates meshes with intricate geometries and arbitrarily shaped elements. The paper discusses the computational efficiency of VEM RBTO and explores the geometric impact of tessellations on converged topologies, demonstrating reduced susceptibility to checkerboard patterns compared to conventional quadrilateral elements. Additionally, the single-loop approach is examined, showcasing comparable accuracy to the first-order/second-order reliability methods (FORM/SORM) of RBTO using VEM. Numerical results for several problems that demonstrate the feasibility of the proposed method are presented. [ABSTRACT FROM AUTHOR]

In this paper, we survey selected software packages for the numerical solution of boundary value ODEs (BVODEs), time-dependent PDEs in one spatial dimension (1DPDEs), and initial value ODEs (IVODEs). A unifying theme of this paper is our focus on software packages for these problem classes that compute error-controlled, continuous numerical solutions. A continuous numerical solution can be accessed by the user at any point in the domain. We focus on error-control software; this means that the software adapts the computation until it obtains a continuous approximate solution with a corresponding error estimate that satisfies the user tolerance. The second section of the paper will provide an overview of recent work on the development of COLNEWSC, an updated version of the widely used collocation BVODE solver, COLNEW, that returns an error-controlled continuous approximate solution based on the use of a superconvergent interpolant to the underlying collocation solution. The third section of the paper gives a brief review of recent work on the development of a new 1DPDE solver, BACOLIKR, that provides time- and space-dependent event detection for an error-controlled continuous numerical solution. In the fourth section of the paper, we briefly review the state of the art in IVODE software for the computation of error-controlled continuous numerical solutions. [ABSTRACT FROM AUTHOR]

In this paper we consider second order iterative boundary value problem with Sturm Liouville type boundary conditions and establish the existence of countably many positive symmetric solutions by using Krasnoselskii's fixed point theorem for operator on a cone. [ABSTRACT FROM AUTHOR]

The bioconvective flows are truly connected to real-life and engineering development. So, the models of biomicrosystems and biocells are considered for the technical analysis in this paper. Our intention for the current analysis was to theoretically examine electrical conduction flow into mass and heat transfer by an extensive gyrotactic microorganism into an inclined magnetic field toward a vertical stretching sheet with nonlinear solar radiation with different solar thermal appliances. The effect on velocity slip and Joule heating was again studied in detail. This classical problem on Navier Stokes equations to the current imitation was decreased to ordinary differential equations by applying the comparison method. The numerical solutions were changed by boundary value problem (BVP) to clarify the subject into finite difference numerical scheme by applying MATLAB. The important results show that the density of motile microorganisms reduces to the bioconvection Lewis number and Peclet number, although reverse performance was noticed for the bioconvection Rayleigh number. Further, solar radiation fosters heat transport. In this paper, complete analysis is provided for potential functions of solar thermoelectric cells, solar ponds, solar thermal power fabrication, etc. [ABSTRACT FROM AUTHOR]

This paper develops the mathematical apparatus of studying control problems for the stationary model of magnetic hydrodynamics of viscous heat-conducting fluid in the Boussinesq approximation. These problems are formulated as problems of conditional minimization of special cost functionals by weak solutions of the original boundary value problem. The model under consideration consists of the Navier–Stokes equations, the Maxwell equations without displacement currents, the generalized Ohm's law for a moving medium and the convection-diffusion equation for temperature. These relations are nonlinearly connected via the Lorentz force, buoyancy force in the Boussinesq approximation and convective heat transfer. Results concerning the existence and uniqueness of the solution of the original boundary value problem and of its generalized linear analog are presented. The global solvability of the control problem under study is proved and the optimality system is derived. Sufficient conditions on the data are established which ensure local uniqueness and stability of solutions of the control problems under study with respect to small perturbations of the cost functional to be minimized and one of the given functions. We stress that the unique stability estimates obtained in the paper have a clear mathematical structure and intrinsic beauty. [ABSTRACT FROM AUTHOR]

In this paper we study an inverse boundary value problem for the biharmonic operator with first order perturbation. Our geometric setting is that of a bounded simply connected domain in the Euclidean space of dimension three or higher. Assuming that the inaccessible portion of the boundary is flat, and we have knowledge of the Dirichlet-to-Neumann map on the complement, we prove logarithmic type stability estimates for both the first and the zeroth order perturbation of the biharmonic operator. [ABSTRACT FROM AUTHOR]

During hurricanes or typhoons, wave forces acting on low-lying coastal bridges can cause significant damage to their decks. However, current research has paid little attention to the impact of topography on wave forces. This paper aimed to propose an analytical model based on potential flow theory to analyze the impact of topography on wave forces on bridge decks. The model employs the eigenfunction-matching method to solve the boundary value problem of waves acting on bridge decks over a step bottom. The validity of the model was confirmed by comparing it with published hydrodynamic experiment results. We also examined the effect of the truncation order on wave forces and selected a proper truncation order. The wave forces on the bridge deck located ahead or behind the bottom step were calculated. This study examined the water depth, distance from the bottom step to the bridge deck, and coastal boundary on wave forces. The calculated results indicate that the coastal boundary would significantly influence wave forces on bridge decks, especially for long-period incident waves. The wave forces can be mitigated by an optimized configuration of the wave–structure–topography system. This paper contributes to understanding the impact of topography on wave forces acting on bridge decks during extreme wave conditions and provides insights into optimizing the design of coastal bridges. The proposed analytical model can supply preliminary guidance at the initial stage of bridge design without costly numerical simulations or physical model tests. [ABSTRACT FROM AUTHOR]

This paper aims to investigate a class for nonlocal fractional boundary value problem on an infinite interval due to its importance in provide a powerful tool for mathematical modeling of complex phenomena in science. New existence results are acquired for the given problem by using the Krasnosel'skii's fixed point theorem. Moreover, sufficient conditions are obtained as well as a modified compactness criterion that guarantees the existence of at least one solution. In addition, an illustrative example is given in the final part of the paper. [ABSTRACT FROM AUTHOR]

In this paper, a high order accuracy method is developed for finding the approximate solution of two-point boundary value problems. The present approach is based on a special algorithm, taken from Pascal’s triangle, for obtaining a generalized form of the parametric splines of degree (2k + 1), k = 1, 2, . . ., which has a lower computational cost and gives the better approximation. Some appropriate band matrices are used to obtain a matrix form for this algorithm. The approximate solution converges to the exact solution of order O(h4k ), where k is a quantity related to the degree of parametric splines and the number of matrix bands that are applied in this paper. Some examples are given to illustrate the applicability of the method, and we compare the computed results with other existing known methods. It is observed that our approach produced better results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper the influence of material imperfections, in the form of small delamination damage, thickness variations and boundary conditions on the fracture behavior of singly and multiply delaminated plates subject to quasi-static out of plane loading is investigated. To simplify the problem and highlight relevant mechanisms, cylindrical bending deformation is assumed and the problem is solved using a semi-analytic model, based on Timoshenko beam theory, that includes relative rotations of the sublaminates at the delamination tips to account for near tip deformations. The results show that the presence of small delamination damage, consisting of an array of small parallel delaminations, induces phenomena of amplification and shielding of the energy release rate of a main delamination propagating through the damaged area. The damage also leads to modification of the mode ratio. Similar phenomena are observed in plates with geometric discontinuities, which are idealizations of stiffeners, patches and cross section variations. These behaviors are controlled by the boundary and loading conditions. [Copyright &y& Elsevier]

The paper deals with the solvability analysis of boundary value problems for degenerate higher-order quasi-hyperbolic equations. The problems in question have the specific feature that the manifolds on which the equations characteristically degenerate are not freed from carrying boundary data. The aim of this paper is to prove the existence and uniqueness of regular solutions of the problems under study, that is, solutions all of whose generalized derivatives occurring in the corresponding equations exist as generalized derivatives in the sense of Sobolev. [ABSTRACT FROM AUTHOR]

This paper concerns with a Lyapunov-type inequality for the Riesz-Caputo fractional boundary value problem with anti-periodic boundary conditions. As an application for the obtained inequality, a lower bound for the eigenvalues of anti-periodic fractional boundary problems of the Riesz-Caputo derivative has been obtained. [ABSTRACT FROM AUTHOR]

Topology optimization (TO) has become increasingly popular as a useful tool for designers and engineers during the initial stages of design. TO aims to optimize the geometry of a design to achieve a specific objective, which can range from discrete grid-like structures to continuum structures. In essence, the geometry is parameterized pixel-by-pixel, with the material density of each element or mesh point serving as a design variable. After that, the optimization problem is addressed using mathematical programming and analytic gradient calculation-based optimization approaches. In this paper, we investigate the material distribution when performing topology optimization for an isotropic material with boundary conditions including fixed structures, supports, or external forces changing. In addition, we investigate more cases where there are material holes in the design domain, meaning that the density of the material is zero. In this study, the modified SIMP method and filter sensitivity are used for topology optimization. The results of the study are the optimized structural domains and the change in compliance according to the number of iterations. The results indicate that the compliance value of most structures reaches convergence after optimization up to the 20th iteration. Moreover, if the force applied to the design domain is symmetrical, the optimal structure also exhibits symmetry. Thus, the distribution of material is concentrated at the positions of the supports. Topology optimization produces designs that both meet boundary conditions while saving material and reducing their mass. The results obtained are important data for structural optimization design for isotropic elastomeric materials. From there, it can be applied to real objects with different requirements and conditions. [ABSTRACT FROM AUTHOR]